Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104780 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. C2×#19104731 | C2 | semidirect |
| 4. #23781835 | C2 | direct (N × H) |
| 5. C2×#19104661 | C2 | semidirect |
| 6. C2×#100×C163 | C2 | semidirect |
| 9. #19104780 | C22 | semidirect |
| 12. C22×D652 | C22 | semidirect |
| 17. #19104763 | C22 | semidirect |
| 21. #19104731 | C22 | semidirect |
| 22. C2×C4×Dic163 | C22 | semidirect |
| 23. #19104661 | C22 | semidirect |
| 25. C2×M16×C163 | C22 | semidirect |
| 26. #100×C163 | C22 | semidirect |
| 31. #14579699 | D4 | semidirect |
| 35. C2×Dic326 | D4 | semidirect |
| 39. C2×D652 | D4 | semidirect |
| 40. C2×D652 | C23 | semidirect |
| 55. C4×Dic163 | C23 | semidirect |
| 63. M16×C163 | C23 | semidirect |
| 73. Dic326 | C2×D4 | semidirect |
| 77. D652 | C2×D4 | semidirect |
| 122. C2×C163 | #453 | semidirect |
| 126. C163 | C2×#453 | semidirect |
| 133. C2×#100 | D163 | semidirect |
| 148. C2×M16 | C2×D163 | semidirect |
| 153. #100 | C2×D163 | semidirect |
| 188. M16 | C22×D163 | semidirect |
| 251. C2 | #23781835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104763 | 2 |
| C2×#19104731 | 2 |
| #23781835 | 2 |
| C2×#19104661 | 2 |
| C2×#100×C163 | 2 |
| C2×#453 | 163 |